1. Field of the Invention
A forecasting field of a seismic event, getting hold of a condition of an activity of the earth""s crust, precaution of an accident in accordance with a seismic event, and reduction thereof.
2. Description of the Background Art
There has been a patent application using an electromagnetic method in Japan. On the contrary, there has been no method of forecasting a seismic event registered a magnitude of more than 5 and a narrow region by way of a value of magnitude indicating a seismic scale, the time of the seismic event, and the position of the seismic source, using a seismograph for measuring in a wide area.
The term xe2x80x9cseismic sourcexe2x80x9d as used herein means xe2x80x9cseismic hypocenterxe2x80x9d and not xe2x80x9cepicenter.xe2x80x9d
The present invention is to find the state of being possible and the significant condition of being related between seismic events registered a magnitude of more than 5, using the value of magnitude indicating a seismic scale, the time of the seismic events, and the position of seismic sources, which have been obtained by a seismograph, and to provide a method therefor.
(1) Seismic data as fundamental data are defined as x(t), y(t), and z(t), by defining x as latitude, y as longitude, z as depth from the earth""s surface by defining coordinates of positions of a seismic source as a time t. The value of magnitude of the earthquake of the same seismic event is defined as m(t).
(2) The positions of the coordinates for measured data during the time between a time t1 and a time t2 are defined as sx(tt1), sy1(tt1), and sz1(tt1) in an early order using a parameter tt1. The value of magnitude of the same earthquake is defined as mx1(tt1). It is considered that the parameter tt1 is equal to the number of the seismic events for calculating after the time t1.
That is to say, data of the 10-th seismic event from the time t1 are sx1(10), sy1(10), sz1(10), and mx1(10). They are fundamental data, thus it is recommended to store in a computer readable recording medium in a time series order. At this stage, for calculating, the range of time, the scope of space, and the scope of magnitude of the earthquake are not designated.
(3) The scope of magnitude of the earthquake, the scope of space coordinates, and the range of time of the measured data are designated. The range of time is indicated as the range from t3 to t4. The case in which a time t4 is the newest data in view of time among obtained data is included. The total number of the seismic events satisfying this condition is defined as nn. It is defined that xe, ye, and ze of the seismic events satisfying this condition are latitude, longitude, and depth from the earth respectively, and they are defined as xe(tt2), ye(tt2), and ze(tt2) respectively. The value of magnitude of the earthquake of the same event is defined as me1(tt2). A parameter tt2 is the number of the seismic event as a target in an early order. Therefore, it is performed to calculate based on these values. For the scope of magnitude of the earthquake, though it is enough regularly to provide the lower limit, it may also be possible to provide the upper limit if there are wrong data (there is a magnitude of 9.9) or if a specific purpose is planned.
(4) For x, y, and z (3 dimensional coordinates of the seismic source), it is common that raw data are indicated by latitude and longitude in accordance with the 3 dimensional space coordinates of the paragraph (3), thus it is performed to transform in order to make into the same unit (kilometer is used in general as the unit).
(5) The basic points (which are indicated by points) to be set first of all about xe(tt2), ye(tt2), and ze(tt2) are defined as xe(0), ye(0), and ze(0). The value of tt2 varies from 1 to nn.
It is performed to calculate ss0(tt2){circumflex over ( )}2=((xe(tt2)xe2x88x92xe(tt2xe2x88x921)){circumflex over ( )}2)pa+((ye(tt2)xe2x88x92ye(tt2 ))xe2x88x92ye(tt2xe2x88x921)){circumflex over ( )}2)pb+(ze(tt2)xe2x88x92ze(tt2xe2x88x921)){circumflex over ( )}2. Symbols pa and pb are coefficients in order to adjust to a unit of ze(tt2).
In general, since depth indicated by ze(tt2) is indicated by kilometer, it is unified by making into a common length unit. xe2x80x9c{circumflex over ( )}xe2x80x9d is an operational symbol for indicating a power.
It is defined that ss0(tt2) is the value of a plus value of the square root of ((xe(tt2)xe2x88x92xe(tt2xe2x88x921)){circumflex over ( )}2)pa+((ye(tt2)xe2x88x92ye(tt2xe2x88x921)){circumflex over ( )}2)pb+(ze(tt2)xe2x88x92ze(tt2xe2x88x921)){circumflex over ( )}2.
(6) If the number of the seismic events for the period is defined as 5 in a uniform manner, the total number of periods come to be more than (nn/5). However, it is desirable to round up in the case in which fractions are found or produced. Accordingly, it is not performed to exclude data of fractions. The total number of periods which are defined in this way is defined as n2. The indication of the number for the period, in accordance with this period, is defined as I.
(7) If the number of the seismic events used for one period is defined as f, ss1(I)=[sigma] ss0(tt2)/f is defined ([sigma] indicates the total number which varies from I=1 to the last period number n. This is not the total number n2 for the period) [sigma] is an operator for indicating the total number which varies from I=1 to the last period number n. In general, the meaning thereof is the same as a capital letter sigma of a Greek letter used in mathematics.
In other words, in the case in which it is performed to divide at the first diving point from the first period per f partitions without causing fractions, ss1(1)=(ss0(1)+ss0(2)+ . . . +ss0(f))/f and ss1(2)=(ss0(f+1)+ss0(f+2)+ . . . +ss0(f+f))/f are obtained. Though the parameter f varies from 1 to n2, if the value of f is too large, the results will have intervals. If the value of f is too small, we cannot help having the results as that we cannot see the wood for the trees. For the first ss0(1), the distance from a spatial base which has been set in the first place is calculated. This calculated result is defined as ss0(1). However, even if they are calculated in the same way, for xe(1), ye(1), ze(1), and me1(1) (the first data), by setting these as spatial bases and by excluding me1(1) from the target of calculating its energy, the essential qualities of its calculation are not affected (however, immediately thereafter, its calculation is affected, especially, in the case in which the number of data is small).
(8) A calculating method in relation to getting hold of a space of the seismic source different from the paragraphs (5), (6), and (7), by obtaining the relative distance from its base based on the spatial base to data (xe(tt2), ye(tt2), ze(tt2)) as the target for calculation, is the method of setting a base for calculating per the partitioning unit indicated in the paragraph (6), based on the values thereof. In another way, the method thereof is to make the shortest distance or the vertical distance from a line and a face to be a base for its calculation. There is a difference between the line and the face: the line to be the base is a line which is indicated as an active fault in a geological figure; and the face is analyzed in relation to a spatial distribution based on the distance from a geophysical base and the face of the active fault.
The advantageous point thereof is to easily find out a blind spot in the case of using ss1(I) if xe(tt2), ye(tt2), and ze(tt2) which have been used in the paragraph (5) are used. In the case in which the spatial base is the line or the face, an expression for indicating the line and the space is created by setting latitude, longitude, and depth as the 3 dimensional coordinate bases, and then the distance from the line and the face is calculated. The units of the distance are unified.
(9) The distance from the bases about xe(tt2), ye(tt2), and ze(tt2) is obtained using data which satisfy the scope of magnitude, the range of time, and the scope of the space which are set in the paragraph (5) of exemplifying the paragraph (8). In the case in which the base is defined as a point, the coordinates as latitude, longitude, and depth of the point to be the bases are defined as xe(0), ye(0), and ze(0) respectively.
ssq0(tt2){circumflex over ( )}2=((xe(tt2)xe2x88x92xe(0)){circumflex over ( )}2)pa+((ye(tt2)xe2x88x92ye(0)){circumflex over ( )}2)pb+(ze(tt2)xe2x88x92ze(0)){circumflex over ( )}2 is calculated.
The value of tt2 varies from 1 to nn. The coefficients pa and pb are used so as to adjust to a unit of ze(tt2). In general, since depth which is indicated by ze(tt2) is indicated by kilometer, the common length is used so as to justify.
For ssq0(tt2), the plus value of the square root of ((xe(tt2)xe2x88x92xe(0)){circumflex over ( )}2)pa+((ye(tt2)xe2x88x92ye(0)){circumflex over ( )}2)pb+(ze(tt2)xe2x88x92ze(0)){circumflex over ( )}2 is used.
(10) If the number of the seismic events for one period is defined as f, ssq1(I)=[sigma] ssq0(tt2)/f is defined. The value of I varies from 1 to n2. In other words, in the case of dividing at the first dividing point per f partitions without causing fractions from the first partition, ssq1(1)=(ssq0(1)+ssq0(2)+ . . . +ssq0(f))/f and ssq1(2)=(ssq0(f+1)+ssq0(f+2)+ . . . +ssq0(f+f))/f are obtained. Though the value of f varies from 1 to n2, if the value of f is too large, the results of calculation will have intervals. If the value of f is too small, we cannot help having the results as that we cannot see the wood for the trees.
(11) Though the difference between the calculating method for the space distribution of the seismic source of the paragraphs (5), (6), and (7) and the calculating method of the paragraphs (8), (9), and (10) for the space distribution of the seismic source is in that the calculation starting point set in the first place affects only the first data (xe(1), ye(1), and ze(1)) for the paragraphs (5), (6), and (7), the calculating methods which have been indicated in the paragraphs (8), (9), and (10) which have described the difference of analyzing the space distribution based on the distance from the spatial base set in the first place in relation to data for the seismic positions in the paragraphs (8), (9), and (10) may make it easy to find out a blind spot in the case of using ss1(I) if xe(tt2), ye(tt2), and ze(tt2) which have been used in the paragraph (5) are used.
In the case in which the spatial bases are the line and the face, an expression of indicating the line and the face is created by defining latitude, longitude, and depth as 3 dimensional coordinate bases, and then the distance from the line and the face is calculated. The unit of the distance is unified. In general, kilometer is used therefor.
(12) For me1(tt2), that is to say, magnitude which indicates energy of the earthquake, the upper and lower limits of magnitude of the seismic events are defined.
The value of total energy of the seismic events in the range of the period of the event is obtained from the value me1(tt2) of each earthquake. The expression used herein is a general expression log E=a+bM for calculating magnitude indicating energy of the earthquake. A unit of the value E of energy therefor is erg of seismology. The value M indicates the value of magnitude indicating the scale of the earthquake. Though the values a and b are not the same in accordance with the region, 1.5 is used for b in general.
Further, in addition thereto, an expression of log means a logarithm with 10 as the base. Further, the methods of calculating magnitude are not the same seismologically corresponding to a way of applying seismic data and a characteristic of the earth of its place.
Further, the total energy ee1(I) of the earthquake in the range of the period is 10{circumflex over ( )}(a+b(M1))+10{circumflex over ( )}(a+b(M2))+ . . . , and the sum total is eel(I). The value sme1(I) of magnitude is obtained, which corresponds to the value ee1(I) of energy in the region of the period. That is to say, sme1(I)=(log(ee1(I))xe2x88x92a)/b is obtained. The logarithm log in this case is the logarithm with 10 as the base for defining magnitude.
Further, for calculating this energy, the value of er1(I)=log(sme1(I+1)/sme1(I)) is used in [numerical expression 2]. In the case of using [numerical expression 3], needless to say, an absolute value, plus, or minus of (er1(I)xe2x88x92er1(I+1)) is important to the values a and b. However, as a matter of course, a and b for calculating magnitude are unified, except that the physical definition and meaning of data for using are changed.
(13) The index is obtained from ee1(I) or sme1(I) obtained in the paragraph (12) and ss1(I) and ssq1(I) obtained in the paragraphs (7), (8), and (9).
[numerical expression 1] [numerical expression 2]
(14) Though there have been data per the period in the case of the paragraph (6), the result of calculating data for the period might be equal to (ss1(I), or ssq1(I), or sme1(I) is 0 (zero) as the definition). Since an inconvenience is caused for calculating the logarithm, a counterplan is required. In such a case, it is recommended to change the length (the period of the event) of the period or the base point for starting calculation, in the case of using ssq1 (I).
In another way, for the value when sr1(I) and srq1(I) indicated by [numerical expression 1] are ∞, for example, +100 and xe2x88x92∞, it is recommended to avoid the condition, in which it is not possible to define, using xe2x88x92100, for example. In the case in which sme1(I) is 0, ee1(I) is used by unifying. In general, such a case is not caused by the current data.
(15) Further, the values ss0(I), ss1(I), ssq0(I), ssq1(I), me1(I), ee1(I), and sme1(I) which are obtained at the stages of obtaining respective periods are also kept. Especially, for ss1(I), ssq1(I), ee1(I), and sme1(I), these are required at the time of indicating the results of calculation or at the time of calculating [numerical expression 3].
(16) Dd1(I), Ddq1(I), and [numerical expression 3] are defined as follows.
(17) Using computer, it is convenient to display visually by setting the period in a horizontal axis, plotting changes of sr1(I), ssrr1(I), srq1(I), ssrqr1(I), sme1(I), er1(I), ssrr1(I), Dd1(I), and Ddq1(I) in the vertical axis by changing magnification suitably, coloring, and the like, and then linking them.
The horizontal axis may be used for a time interval, or the same horizontal axis may be used per the period.
[numerical expression 1] Liapunov coefficients:
sr1(I)=log(ss1(I+1)/ss1(I)):
ssr1(n)=[sigma] sr1(I): srq1(I)=log(ssq1(I+1)/ssq1(I)):
ssrq1(n)=[sigma] srq1(I):
ssrqr1(n)=[sigma] srq1(I)/n:ssrr1(n)=[sigma] sr1(I)/n: log with as the base. ([sigma] defines the sum total for I=1 to the last period number n. This not the sum total n2 of periods. [sigma] is an operator indicating the sum total for I=1 to the last period number n.) In general, this has the same meaning as a capital letter sigma of a Greek letter used in mathematics.
The meaning of ssr1(n)=[sigma] sr1(I) has the meaning of ssr1(n)=sr1(1)+sr1 (2)+ . . . +sr1 (n). The value n has the values of 1 to (n2xe2x88x921).
[numerical expression 2] It is possible to substitute ee1(I) for sme(I) when calculating
Liapunov coefficients:
er1(I)=log(ee1(I+1)/ee1(I)):
ser1(n)=[sigma] er1(I):ssrr1(n)=[sigma] er1(I)/n. Both of them have the same essential values. The value of n has the values of 1 to (n2xe2x88x921).
[numerical expression 3] Dd1(I)=(er1(I)xe2x88x92er1(I+1))(sr1(I)xe2x88x92sr1(I+1))
Ddq1(I)=(er1(I)xe2x88x92er1(I+1))(srq1(I)xe2x88x92srq1(I+1)) The meaning of Dd1(I) has the meaning of the product of (er1(I)xe2x88x92er1(I+1)) and (sr1(I)xe2x88x92sr1(I+1)). The same relation is found in Ddq1(I). The value I has the values of 1 to (n2-2).